The short answer if you can own domain forever is no. You can’t buy a domain and own it forever. But you can buy a domain for a longer time period.
For example, if you check on the website of domain registrars Namecheap you will see that you can buy the domain for a period of 10 years.
The price for a longer period is usually cheaper as the renewing domain every year but be careful every domain registrar has its own rules.
Example of Namecheap .com domain is more expensive for 10 years period (calculation per year):
If you buy the .com domain each year this will cost you $8.88 per year.
If you buy the domain for 10 years it will cost you: $105.80 for a period of 10 years. $10.58 per year.
One of the options, when you are buying a domain name, is the AUTO-RENEW option.
Auto-renew option means that every year a domain registrar will automatically renew your domain name if you have enough money on your credit card. You can always turn off an auto-renew option usually inside the domain registrar control panel. The auto-renew option can be cheaper as buying the domain for a longer time period.